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maxiee

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## Homework Statement

Mathematically, the Azimuthal equation is the same differential equation as the one for a particle in a box. But [tex] \Phi(\phi) [/tex] for [tex] m_l = 0 [/tex], is a constant and is allowed, whereas such a constant wave function is not allowed for a particle in a box. What physics accounts for the difference?

## Homework Equations

The Azimuthal Equation:

[tex]

\frac{\partial ^{2} \Phi(\phi)}{\partial \phi^{2}} = -m_l ^{2} \Phi(\phi)

[/tex]

The particle in a box equation:

[tex]

\frac{\partial ^{2} \psi(x)}{\partial \psi^{2}} = -k ^{2} \psi(x)

[/tex]

## The Attempt at a Solution

The boundary conditions seem to play a role in the different allowed wave functions. However, I am having trouble relating the boundary conditions to the allowed quantum numbers.

Thanks in advance

Edit: The Azimuthal Equation corresponds to the Azimuthal motion of a particle. It comes about from the 3D Schrodinger Eq.

The Equation for a particle in a box is the result of the 1D Schrodinger Eq.

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